Manufacturing and other processing systems typically involve changing the value of one or more control variables, including but not limited to temperature, pressure, gas flow rates, concentration, tension, voltage, applied force, and position. The rate at which a control variable is changed from a starting value to an ending value is the ramp rate or first derivative of that variable, known generically as the ramp rate. For instance, the ramp rate or first derivative of position with regards to time (such as dx/dt) is velocity. It is often desirable to minimize stresses to which equipment and/or products are exposed during a process. Excess stress can lead to reduced efficiency of a process or to premature failure of equipment or products. In many systems, stresses are a function of the ramp rate of one or more control variables. The ramp rate may be reduced to maintain stress below an acceptable threshold. However, unnecessarily severe ramp rate limits are also undesirable because they slow process throughput. An illustrative example of this concept is drawn from semiconductor processing systems. It should be noted, however, that ramp-rate related problems are not unique to the application discussed in detail herein. Rather, the examples are meant to be merely illustrative and not limiting in any way.
An important aspect in the manufacture of semiconductors and integrated circuits is the temperature variations and values that semiconductor wafers are subjected to during processing. Two important limitations apply to heating and cooling of semiconductor wafers: 1) acceleration and deceleration of the temperature ramp rate cannot occur more rapidly than the thermal inertia of the wafer will permit and 2) the temperature difference between the center and edge of a wafer should be kept sufficiently small to prevent thermal expansion damage to the wafer. Thermal inertia describes the resistance of a mass to instantaneously jumping from a steady-state temperature or zero ramp rate state to a finite non-zero ramp rate and back to steady state again. Real objects are incapable of the instantaneous and infinite “acceleration” and deceleration” in temperature ramp rates that are necessary to heat or cool under these idealized requirements. Temperature acceleration or deceleration is the second time derivative of temperature. Just as for positional acceleration and deceleration of a mass at rest, the temperature acceleration and deceleration rates cannot be infinite.
When heating or cooling from one temperature to another within a furnace, such as a semiconductor wafer processing system, it is often important to reach the desired setpoint temperature in a minimum amount of time. Classically, a furnace will use a controlled linear ramp to go from one temperature setpoint to another. Linear ramping is plagued by two disadvantages: a delay in attainment of the desired temperature ramp rate by the substrate being heated; and a tendency for the temperature of the substrate to overshoot the desired setpoint and then oscillate around the set point temperature before achieving a steady state temperature. A solution to this problem employing physically attainable temperature ramp rate acceleration and deceleration phases is described in copending U.S. patent application Ser. No. 10/068,127, the text of which is incorporated herein by reference.
Of additional importance is limiting the maximum temperature ramp rate to protect against negative thermal effects on the object or objects being heated due to excessive internal temperature gradients within the object. This is of particular concern in semiconductor wafer processing systems in which important manufacturing aspects are the temperature variations and values that the semiconductor wafers are subjected to during processing. In particular, the temperature difference between the center and the edge of the wafer during processing in a rapid thermal processing furnace or other similar equipment is of significant interest since excessive heating or cooling of the edge of a wafer relative to its center can result in physical and/or chemical damage that could render the wafer unuseable or lead to early failure of semiconductor chips manufactured from the wafer. This edge-center temperature difference is referred to as the radial delta temperature, or radial delta-T (RDT). The problem particularly affects batch furnaces, which apply heat to the outside edge of a stack of wafers. During heating with a radiative heat source such as a resistive heating coil or a heat lamp, the wafer edges may, at times, be several degrees (or even tens of degrees) hotter than the center of the wafer because radiative heat transfer is greatest at the wafer edges. Conversely, during cooling, the edges undergo more rapid heat loss through radiative cooling and thus may be substantially cooler than the wafer centers. At high temperatures, this RDT may induce crystal slip on the wafer.
The advantages of limiting temperature ramp rates to minimize thermal expansion stress induced crystal slip damage on semiconductor substrates is well known. It is desirable to minimize the RDT during processing to minimize excess thermal stress occurring on the substrate. The temperature ramp rate during processing is the primary factor in determining the RDT. At higher ramp rates, the thermal inertia of a substrate being heated can further exacerbate the temperature variations between its edge and its center as heat applied to the edges is not instantaneously conducted to the center of the substrate. At lower temperatures, a larger RDT can be tolerated without causing excess thermal stress because silicon atom-to-atom bonds are stronger and can withstand more thermal stress at lower temperatures. Thus, it is desirable to provide a system and method for the control of RDT across a substrate. To avoid exceeding the maximum allowable thermal stress on a wafer, prior art methods rely on manually programmed sequences of fixed ramp rates. This approach prevents the process from functioning at the maximum possible ramp rate throughout a heating or cooling process because the actual maximum allowable ramp rate to avoid RDT-induced thermal stress damage varies with temperature as noted above. Furthermore, this segmented ramp rate profile can also result in ramp rates that exceed the allowable maximum RDT for a given temperature. Heating with a noncontinuous temperature ramp profile therefore deviates from the ideal maximum ramp rate curve.
Accordingly an improved system and method of temperature control is needed to govern the ramp rate as a function of the temperature of a body or substrate being heated or cooled.